Question

Find the inverse of the radical function t[3]{x-2}" alt="\sqrt[3]{x-2}" align="absmiddle" class="latex-formula">

Answer 1

Answer: y=x³+2 or f⁻¹(x)=x³+2

Step-by-step explanation:

To find the inverse of the radical function, we replace y with x and x with y. Then, you solve for y.

$y=\sqrt[3]{x-2}$                        [replace y with x and x with y]

$x=\sqrt[3]{y-2}$                        [cube both sides to cancel out the cubed root]

$x^3=y-2$                          [add both sides by 2]              

$x^3+2=y$

Now that we have switched the variables and solved for y, we know that the inverse function is y=x³+2 or f⁻¹(x)=x³+2.